A coalition led by the BJP, which captured 86 of the 126 seats in the northeastern state’s legislature, according to official results announced Thursday, knocked the Congress party from one of its few remaining perches. Once a major political force, the left-leaning Congress’s slide has accelerated since Mr. Modi’s 2014 national election win.

A tweet posted on Mr. Modi’s verified account Thursday congratulated his party’s workers on what he called an “exceptional” victory. “This win is historic by all standards,” he said.

Taking control of Assam will help the BJP regain some momentum after losses in two state polls last year. BJP defeats in Delhi and Bihar raised questions about whether Mr. Modi’s popularity was waning and whether he would be able to push his economic agenda forward.

The BJP—long considered a northern Indian party with an urban and upper-caste base—has launched a major effort to spread to parts of the country where it has so far only been a marginal player. Thursday’s results showed both its progress and challenges.